Bayesian D-optimal Accelerated Life Test plans for series systems with competing exponential causes of failure

Abstract

This paper provides methods of obtaining Bayesian D-optimal Accelerated Life Test (ALT) plans for series systems with independent exponential component lives under the Type-I censoring scheme. Two different Bayesian D-optimality design criteria are considered. For both the criteria, first optimal designs for a given number of experimental points are found by solving a finite-dimensional constrained optimization problem. Next, the global optimality of such an ALT plan is ensured by applying the General Equivalence Theorem. A detailed sensitivity analysis is also carried out to investigate the effect of different planning inputs on the resulting optimal ALT plans. Furthermore, these Bayesian optimal plans are also compared with the corresponding (frequentist) locally D-optimal ALT plans.

Keywords:

• constrained optimization
• Fisher information
• General Equivalence Theorem
• prior information
• sensitivity analysis

AMS Subject Classification:

• 62K05
• 62N05

Acknowledgments

The authors would like to thank two anonymous referees for their valuable comments, which greatly enhanced the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.